Finite Group Databasebeta

← C3×#9163 #10627770

Subgroups — C3×#9163 #10627770

Order 768.

508 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3109C211yesmaximal, characteristic
2C3×#2974C211yesmaximal, characteristic, complemented
3C3×#1762C211yesmaximal, characteristic, complemented
4C3×#1530C211yesmaximal, characteristic, complemented
5C3×#1502C211yesmaximal, characteristic, complemented
6C3×#1302C211yesmaximal, characteristic, complemented
7C3×#1285C211yesmaximal, characteristic, complemented
8#9163C311yesmaximal, characteristic, direct product factor, Sylow
9C3×#532C2211yescharacteristic
10C2×C3×C4×D4C2211yescharacteristic
11C3×#481—21no—
12C3×#476C411yescharacteristic, complemented
13C3×#476C411yescharacteristic, complemented
14C3×#459C411yescharacteristic, complemented
15C3×#459C411yescharacteristic, complemented
16C3×#447—21no—
17C3×#442—21no—
18C3×#442—21no—
19C3×#436—21no—
20C3×#435—22no—
21C3×C8×D4—21no—
22C3×#432C2211yescharacteristic
23C3×#432C2211yescharacteristic
24C3×#431C2211yescharacteristic
25C2×C3×#102—21no—
26C3×#407—21no—
27C2×C3×C22⋊C8—21no—
28C2×C3×#97C2211yescharacteristic
29C3×C4×C4⋊C4C2211yescharacteristic
30C3×#340—21no—
31C3×#329—22no—
32C3×#327—21no—
33C3×#327—21no—
34#3109C2×C311yescharacteristic
35#2974C2×C311yescharacteristic, complemented
36#1762C2×C311yescharacteristic, complemented
37#1530C2×C311yescharacteristic, complemented
38#1502C2×C311yescharacteristic, complemented
39#1302C2×C311yescharacteristic, complemented
40#1285C2×C311yescharacteristic, complemented
41C2×C3×#41—21no—
42C22×C3×D4D411yescharacteristic
43C23×C3×C4—21no—
44C2×C3×D8—21no—
45C2×C3×D8—21no—
46C2×C3×M16—22no—
47C22×C3×C8—21no—
48C22×C3×C8—22no—
49C3×C4⋊Q8C2×C411yescharacteristic
50C3×#127C2×C411yescharacteristic
51C3×#124—21no—
52C3×#121—21no—
53C3×#121—21no—
54C3×C4×D4—21no—
55C3×C4×D4—21no—
56C3×C4×D4—21no—
57C3×C4×D4—21no—
58C3×C4×D4C2×C411yescharacteristic
59C3×C4×D4C2×C411yescharacteristic
60C3×C4×D4D411yescharacteristic
61C3×C4×D4D411yescharacteristic
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4D411yescharacteristic
64C2×C3×C22⋊C4—21no—
65C2×C3×C42—21no—
66C2×C3×C42C2311yescharacteristic
67C3×#106—21no—
68C3×#106—21no—
69C3×C4⋊C8—21no—
70C3×C4⋊C8—21no—
71C3×C4⋊C8C2×C411yescharacteristic
72C3×C4⋊C8C2×C411yescharacteristic
73C3×#102—24no—
74C3×#102—21no—
75C3×#102—21no—
76C3×#102—21no—
77C3×#102—21no—
78C3×C22⋊C8—22no—
79C3×C22⋊C8—22no—
80C3×C22⋊C8—21no—
81C3×C22⋊C8—21no—
82C3×C22⋊C8D411yescharacteristic
83C3×C22⋊C8D411yescharacteristic
84C3×#97—21no—
85C3×#97—21no—
86C3×#97—21no—
87C3×#97D412yes—
88C3×C4×C8—21no—
89C3×#95—21no—
90#532C22×C311yescharacteristic
91C2×C4×D4C22×C311yescharacteristic
92#481—21no—
93#476C3×C411yescharacteristic, complemented
94#476C3×C411yescharacteristic, complemented
95#459C3×C411yescharacteristic, complemented
96#459C3×C411yescharacteristic, complemented
97#447—21no—
98#442—21no—
99#442—21no—
100#436—21no—
101#435—22no—
102C8×D4—21no—
103#432C22×C311yescharacteristic
104#432C22×C311yescharacteristic
105#431C22×C311yescharacteristic
106C2×#102—21no—
107#407—21no—
108C2×C22⋊C8—21no—
109C2×#97C22×C311yescharacteristic
110C4×C4⋊C4C22×C311yescharacteristic
111#340—21no—
112#329—22no—
113#327—21no—
114#327—21no—
115C24×C3—21no—
116C3×#41—81no—
117C3×#41—81no—
118C2×C3×Q8—21no—
119C2×C3×D4—22no—
120C2×C3×D4—21no—
121C2×C3×D4—21no—
122C2×C3×D4—21no—
123C2×C3×D4—21no—
124C2×C3×D4—41no—
125C2×C3×D4—41no—
126C2×C3×D4C22⋊C411yescharacteristic
127C2×C3×D4C22⋊C411yescharacteristic
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—41no—
134C22×C3×C4—41no—
135C22×C3×C4—82no—
136C22×C3×C4C2×D411yescharacteristic
137C22×C3×C4C2×D411yescharacteristic
138C22×C3×C4#4111yescharacteristic
139C3×D8—42no—
140C3×D8—42no—
141C3×M16—82no—
142C2×C3×C8—22no—
143C2×C3×C8—21no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—22no—
148C2×C3×C8—41no—
149C2×C3×C8—41no—
150C2×C3×C8—82no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—41no—
156C3×C4⋊C4C22⋊C411yescharacteristic
157C3×C4⋊C4C22⋊C411yescharacteristic
158C3×C22⋊C4—21no—
159C3×C22⋊C4—21no—
160C3×C22⋊C4—21no—
161C3×C22⋊C4—21no—
162C3×C22⋊C4—41no—
163C3×C22⋊C4—41no—
164C3×C42—81no—
165C3×C42C22×C411yescharacteristic
166C3×C42C2×D411yescharacteristic
167C3×C42C2×D411yescharacteristic
168C3×C42#4111yescharacteristic
169C2×#41—21no—
170C22×D4C3×D411yescharacteristic
171C23×C4—21no—
172C2×D8—21no—
173C2×D8—21no—
174C2×M16—22no—
175C22×C8—21no—
176C22×C8—22no—
177C4⋊Q8C2×C3×C411yescharacteristic
178#127C2×C3×C411yescharacteristic
179#124—21no—
180#121—21no—
181#121—21no—
182C4×D4—21no—
183C4×D4—21no—
184C4×D4—21no—
185C4×D4—21no—
186C4×D4C2×C3×C411yescharacteristic
187C4×D4C2×C3×C411yescharacteristic
188C4×D4C3×D411yescharacteristic
189C4×D4C3×D411yescharacteristic
190C2×C4⋊C4—21no—
191C2×C4⋊C4C3×D411yescharacteristic
192C2×C22⋊C4—21no—
193C2×C42—21no—
194C2×C42C23×C311yescharacteristic
195#106—21no—
196#106—21no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8C2×C3×C411yescharacteristic
200C4⋊C8C2×C3×C411yescharacteristic
201#102—24no—
202#102—21no—
203#102—21no—
204#102—21no—
205#102—21no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—21no—
209C22⋊C8—21no—
210C22⋊C8C3×D411yescharacteristic
211C22⋊C8C3×D411yescharacteristic
212#97—21no—
213#97—21no—
214#97—21no—
215#97C3×D412yes—
216C4×C8—21no—
217#95—21no—
218C23×C3—21no—
219C23×C3—21no—
220C23×C3—42no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3—41no—
224C23×C3—81no—
225C23×C3#12111yescharacteristic
226C3×Q8—81no—
227C3×D4—21no—
228C3×D4—21no—
229C3×D4—21no—
230C3×D4—42no—
231C3×D4—41no—
232C3×D4—41no—
233C3×D4—81no—
234C3×D4—81no—
235C3×D4—81no—
236C3×D4—81no—
237C3×D4#10412yes—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—41no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—41no—
249C2×C3×C4—81no—
250C2×C3×C4—81no—
251C2×C3×C4—82no—
252C2×C3×C4—81no—
253C2×C3×C4—81no—
254C2×C3×C4—81no—
255C2×C3×C4C2×C22⋊C411yescharacteristic
256C2×C3×C4C4×D411yescharacteristic
257C2×C3×C4C4×D411yescharacteristic
258C2×C3×C4#12011yescharacteristic
259C2×C3×C4#12111yescharacteristic
260C2×C3×C4#12311yescharacteristic
261C3×C8—42no—
262C3×C8—41no—
263C3×C8—42no—
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—41no—
267C24—21no—
268#41—81no—
269#41—81no—
270C2×Q8—21no—
271C2×D4—22no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4C3×C22⋊C411yescharacteristic
279C2×D4C3×C22⋊C411yescharacteristic
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—82no—
288C22×C4C2×C3×D411yescharacteristic
289C22×C4C2×C3×D411yescharacteristic
290C22×C4C3×#4111yescharacteristic
291D8—42no—
292D8—42no—
293M16—82no—
294C2×C8—22no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—82no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4C3×C22⋊C411yescharacteristic
309C4⋊C4C3×C22⋊C411yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—81no—
317C42C22×C3×C411yescharacteristic
318C42C2×C3×D411yescharacteristic
319C42C2×C3×D411yescharacteristic
320C42C3×#4111yescharacteristic
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—22no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—82no—
330C22×C3—82no—
331C22×C3—81no—
332C22×C3—81no—
333C22×C3—81no—
334C22×C3#38611yescharacteristic
335C22×C3#47111yescharacteristic
336C22×C3#47211yescharacteristic
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—82no—
345C3×C4—81no—
346C3×C4C2×#10411yescharacteristic
347C3×C4#42111yescharacteristic
348C23—21no—
349C23—21no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—81no—
355C23C3×#12111yescharacteristic
356Q8—81no—
357D4—21no—
358D4—21no—
359D4—21no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4C3×#10412yes—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—82no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C2×C3×C22⋊C411yescharacteristic
386C2×C4C3×C4×D411yescharacteristic
387C2×C4C3×C4×D411yescharacteristic
388C2×C4C3×#12011yescharacteristic
389C2×C4C3×#12111yescharacteristic
390C2×C4C3×#12311yescharacteristic
391C8—42no—
392C8—41no—
393C8—42no—
394C8—41no—
395C8—41no—
396C8—41no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—42no—
400C2×C3—81no—
401C2×C3—161no—
402C2×C3#187111yescharacteristic
403C2×C3#190411yescharacteristic
404C2×C3#190711yescharacteristic
405C22—21no—
406C22—21no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—82no—
414C22—82no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22C3×#38611yescharacteristic
419C22C3×#47111yescharacteristic
420C22C3×#47211yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—21no—
425C4—21no—
426C4—41no—
427C4—41no—
428C4—82no—
429C4—81no—
430C4C2×C3×#10411yescharacteristic
431C4C3×#42111yescharacteristic
432C3#916311yescharacteristic, direct product factor, Sylow
433C2—21no—
434C2—21no—
435C2—42no—
436C2—81no—
437C2—161no—
438C2C3×#187111yescharacteristic
439C2C3×#190411yescharacteristic
440C2C3×#190711yescharacteristic
subgroupG/H
center, socleC22×C3#386
commutatorC42C22×C3×C4
Frattini, cosocleC2×C42C23×C3
prime radicalC3×#3109C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#2974C2semidirect
3. C3×#1762C2semidirect
4. C3×#1530C2semidirect
5. C3×#1502C2semidirect
6. C3×#1302C2semidirect
7. C3×#1285C2semidirect
8. #9163C3direct (N × H)
12. C3×#476C4semidirect
13. C3×#476C4semidirect
14. C3×#459C4semidirect
15. C3×#459C4semidirect
35. #2974C2×C3semidirect
36. #1762C2×C3semidirect
37. #1530C2×C3semidirect
38. #1502C2×C3semidirect
39. #1302C2×C3semidirect
40. #1285C2×C3semidirect
93. #476C3×C4semidirect
94. #476C3×C4semidirect
95. #459C3×C4semidirect
96. #459C3×C4semidirect
432. C3#9163direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#31092
C3×#29742
C3×#17622
C3×#15302
C3×#15022
C3×#13022
C3×#12852
#91633